Publication number | US5420891 A |

Publication type | Grant |

Application number | US 08/033,604 |

Publication date | May 30, 1995 |

Filing date | Mar 18, 1993 |

Priority date | Mar 18, 1993 |

Fee status | Lapsed |

Publication number | 033604, 08033604, US 5420891 A, US 5420891A, US-A-5420891, US5420891 A, US5420891A |

Inventors | Ali N. Akansu |

Original Assignee | New Jersey Institute Of Technology |

Export Citation | BiBTeX, EndNote, RefMan |

Patent Citations (20), Non-Patent Citations (20), Referenced by (85), Classifications (12), Legal Events (4) | |

External Links: USPTO, USPTO Assignment, Espacenet | |

US 5420891 A

Abstract

The Multiplierless Quadrature Mirror Filter concept is used in the design of analysis and synthesis filter banks to be used for the sub-band coding of various types of signals. The individual filters in the analysis and synthesis filter banks are designed to be near linear in phase, non-symmetrical in time, and to have equal bandwidth frequency responses. These multiplierless filters are relatively easy to implement in hardware and allow for the sub-band coding of signals with minimal computational complexity so as to result perfect signal reconstruction. Furthermore, these filters are particularly well suited for configuration in hierarchical sub-band structures.

Claims(22)

1. A multiplierless filter bank to be used in the sub-band coding of various types of signals, said multiplierless filter bank comprising at least one pair of finite impulse response filters connected in parallel, said finite impulse response filters in each said pair of finite impulse response filters having non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, said finite impulse response filters in each said pair of finite impulse response filters being Multiplierless Quadrature Mirror Filters which satisfy the perfect reconstruction requirement, ##EQU3## wherein Q is an integer normalization factor, wherein

δ(k)=1 for K=0

δ(k)=0 for all other k

wherein N+1 is the order of said Multiplierless Quadrature Mirror Filters, wherein ##EQU4## wherein

n=0, 1, . . .,N

wherein

k_{n}.sup.(i) =integers

and wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said Multiplierless Quadrature Mirror Filters.

2. The multiplierless filter bank as defined in claim 1, wherein said finite impulse response filters in each said pair of finite impulse response filters have equal bandwidth frequency responses such that two equal bandwidth sub-band signals are formed from each of said various types of signals that is applied to each said pair of finite impulse response filters.

3. The multiplierless filter bank as defined in claim 1, wherein said finite impulse response filters in each said pair of finite impulse response filters have linear-like phase responses.

4. The multiplierless filter bank as defined in claim 1, wherein a plurality of said finite impulse response filter pairs are configured in a hierarchical sub-band structure so as to form a plurality of equal bandwidth sub-band signal pairs.

5. The multiplierless filter bank as defined in claim 1, wherein said various types of signals include one-dimensional and multi-dimensional signals.

6. A sub-band coding system for various types of signals, said sub-band coding system comprising:

a first multiplierless filter bank for analyzing each of said various types of signals into a plurality of sub-band signals, wherein said first multiplierless filter bank comprises at least one pair of finite impulse response filters having non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, wherein said finite impulse response filters in each said pair of finite impulse response filters in said first multiplierless filter bank are Multiplierless Quadrature Mirror Filters which satisfy the perfect reconstruction requirement, ##EQU5## wherein Q is an integer normalization factor, wherein

δ(k)=1 for k=0

δ(k)=0 for all other k

wherein N+1 is the order of said Multiplierless Quadrature Mirror Filters, wherein ##EQU6## wherein

n=0, 1, . . .,N

wherein

k_{n}.sup.(i) =integers

and wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said Multiplierless Quadrature Mirror Filters; and

a second multiplierless filter bank, connected in, series with said first multiplierless filter bank, for synthesizing each of said various types of analyzed signals from said plurality of sub-band signals, wherein said second multiplierless filter bank comprises at least one pair of finite impulse response filters having non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, wherein said finite impulse response filters in each said pair of finite impulse response filters in said second multiplierless filter bank are Multiplierless Quadrature Mirror Filters which satisfy the perfect reconstruction requirement, ##EQU7## wherein Q is an integer normalization factor, wherein

δ(k)=1 for k=0

δ(k)=0 for all other k

wherein N+1 is the order of said Multiplierless Quadrature Mirror Filters, wherein ##EQU8## wherein

n=0, 1, . . .,N

wherein

k_{n}.sup.(i) =integers

and wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said Multiplierless Quadrature Mirror Filters.

7. The sub-band coding system as defined in claim 6, wherein said plurality of sub-band signals are decimated by a decimation operator and then coded by a coder after being analyzed by said first multiplierless filter bank.

8. The sub-band coding system as defined in claim 7, wherein said plurality of decimated and coded sub-band signals are decoded by a decoder and then interpolated by an interpolation operator before being synthesized by said second multiplierless filter bank.

9. The sub-band coding system as defined in claim 6, wherein said first multiplierless filter bank comprises at least one pair of multiplierless finite impulse response filters having transfer functions H_{0} (z) and H_{1} (z), and wherein said second multiplierless filter bank comprises at least one corresponding pair of multiplierless finite impulse response filters having transfer functions G_{0} (z)=-H_{1} (-z) and G_{1} (z)=H_{0} (-z), such that said second multiplierless filter bank serves to synthesize a perfect reconstruction of each of said various types of analyzed signals from said plurality of sub-band signals.

10. The sub-band coding system as defined in claim 9, wherein said multiplierless finite impulse response filters in each said pair of multiplierless finite impulse response filters have equal bandwidth frequency responses such that two equal bandwidth sub-band signals are formed from each signal that is applied to each said pair of multiplierless finite impulse response filters.

11. The sub-band coding system as defined in claim 10, wherein said multiplierless finite impulse response filters in each said pair of multiplierless finite impulse response filters have linear-like phase responses.

12. The sub-band coding system as defined in claim 9, wherein a plurality of multiplierless finite impulse response filter pairs are configured in a hierarchical sub-band structure so as to form a plurality of equal bandwidth sub-band signal pairs.

13. The sub-band coding system as defined in claim 9, wherein said various types of signals include one-dimensional and multi-dimensional signals.

14. A sub-band coding system for various types of signals, said sub-band coding system comprising:

at least one pair of finite impulse response Multiplierless Quadrature Mirror Filters (M-QMF's) for analyzing each of said various types of signals into a plurality of analyzed sub-band signals, wherein said finite impulse response M-QMF's in each said pair of analyzing M-QMF's have non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, wherein said finite impulse response M-QMF's in each said pair of analyzing M-QMF's satisfy the perfect reconstruction requirement, ##EQU9## wherein Q is an integer normalization factor, wherein

δ(k)=1 for k=0

δ(k)=0 for all other k

wherein N+1 is the order of said M-QMF's, wherein ##EQU10## wherein

n=1, 1, . . .,N

wherein

k_{n}.sup.(i) =integers

and wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said M-QMF's;

means for decimating each of said analyzed sub-band signals;

means for coding each of said decimated sub-band signals;

means for decoding each of said coded sub-band signals;

means for interpolating each of said decoded sub-band signals;

at least one pair of finite impulse response Multiplierless Quadrature Mirror Filters (M-QMF's) for synthesizing each of said analyzed sub-band signals from said plurality of interpolated sub-band signals, wherein said finite impulse response M-QMF's in each said pair of synthesizing M-QMF's have non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, wherein said finite impulse response M-QMF's in each said pair of synthesizing M-QMF's satisfy the perfect reconstruction requirement,

wherein Q is an integer normalization factor, wherein ##EQU11##

δ(k)=1 for k=0

δ(k)=0 for all other k

wherein N+1 is the order of said M-QMF's, wherein ##EQU12## wherein

n=0, 1, . . .,N

wherein

k_{n}.sup.(i) =integers

and wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said M-QMF's; and

means for summing said synthesized analyzed sub-band signals so as to perfectly reconstruct each of said various types of analyzed signals.

15. The sub-band coding system as defined in claim 14, wherein said finite impulse response M-QMF's in each said pair of analyzing M-QMF's have transfer functions H_{0} (z) and H_{1} (z), and wherein said finite impulse response M-QMF's in each said pair of synthesizing M-QMF's have transfer functions G_{0} (z)=-H_{1} (-z) and G_{1} (z)=H_{0} (-z) corresponding with the transfer functions of said finite impulse response M-QMF's in each said pair of analyzing M-QMF's.

16. The sub-band coding system as defined in claim 14, wherein said finite impulse response M-QMF's in each said pair of analyzing M-QMF's have equal bandwidth frequency responses such that two equal bandwidth sub-band signals are formed from each of said various types of signals that is applied to each said pair of analyzing M-QMF's, and wherein said finite impulse response M-QMF's in each said pair of synthesizing M-QMF's have equal bandwidth frequency responses corresponding with the frequency responses of said finite impulse response M-QMF's in each said pair of analyzing M-QMF's.

17. The sub-band coding system as defined in claim 14, wherein said finite impulse response M-QMF's in each said pair of analyzing M-QMF's have linear-like phase responses, and wherein said finite impulse response M-QMF's in each said pair of synthesizing M-QMF's have linear-like phase responses.

18. A multiplierless filter bank, said multiplierless filter bank comprising at least one pair of finite impulse response filters connected in parallel, said finite impulse response filters in each said pair of finite impulse response filters having non-symmetrical filter coefficients which are decomposable into power of two integers such that filter computations are carried out using only binary shift or binary shift and add operations, said finite impulse response filters in each said pair of finite impulse response filters being Multiplierless Quadrature Mirror Filters which satisfy the perfect reconstruction requirement, ##EQU13## wherein Q is an integer normalization factor, wherein

δ(k)=1 for k=0

δ(k)=0 for all other k

wherein N+1 is the order of said Multiplierless Quadrature Mirror Filters, wherein ##EQU14## wherein

n=0, 1, . . .,N

wherein

k_{n}.sup.(i) =integers

and wherein there is no limit on the value of P, although the lower the value of P the higher the efficiency of said Multiplierless Quadrature Mirror Filters.

19. The multiplierless filter bank as defined in claim 18, wherein said finite impulse response filters in each said pair of finite impulse response filters have equal bandwidth frequency responses such that two equal bandwidth sub-band signals are formed from each signal that is applied to each said pair of finite impulse response filters.

20. The multiplierless filter bank as defined in claim 18, wherein said finite impulse response filters in each said pair of finite impulse response filters have linear-like phase responses.

21. The multiplierless filter bank as defined in claim 18, wherein a plurality of said finite impulse response filter pairs are configured in a hierarchical sub-band structure so as to form a plurality of equal bandwidth sub-band signal pairs.

22. The multiplierless filter bank as defined in claim 18, wherein one-dimensional and multi-dimensional signals are applied to each said pair of finite impulse response filters.

Description

1. Field of the Invention

The present invention relates to signal decomposition and reconstruction in sub-band coding and, more particularly, to analysis and synthesis filter banks that are designed according to the Quadrature Mirror Filter concept such that the sub-band coding of various types of signals may be accomplished with minimal computational complexity so as to result in perfect signal reconstruction.

2. Description of the Prior Art

Sub-band coding refers to a technique wherein, by the parallel application of a set of filters, an input signal is decomposed into a number of narrow band signals that are separately decimated and coded for the purpose of transmission. After transmission the signals are decoded, interpolated, and filtered so as to reconstruct the original signal. Originally, sub-band coding was developed for the transmission of speech signals (see e g. R. E. Crochiere et al., "Digital Coding of Speech in Sub-bands", BSTJ Vol. 55, pp. 1069-1085). More recently, however, sub-band coding has been used for the transmission of video signals (see e.g. J. W. Woods et al., "Subband Coding of Images" IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-34, pp. 1278-1288, October 1986).

When designing a sub-band coding scheme, great emphasis is placed on the selection of analysis and synthesis filter banks. Such analysis and synthesis filter banks are used to decompose and reconstruct, respectively, the original signal. Much of the design work for these filter banks has been motivated by speech signal processing, wherein sharp band separation is a very desirable property. This work has led naturally to finite impulse response (FIR) filter banks with a large number of stages, e.g. 64. A classical approach to designing such filter banks is the Quadrature Mirror Filter approach, which allows substantially exact reconstruction of input speech signals (see e.g. D. Esteban et al., "Application of Quadrature Mirror Filters to Split Band Voice Coding Schemes", Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 191-195, 1977). Application of the Quadrature Mirror Filter concept to the sub-band coding of video signals has recently received considerable attention since it has been shown that this approach is highly effective for image compression (see e.g. M. Vetterli, "Multi-dimensional Sub-band Coding: Some Theory and Algorithms", Signal Processing (1984), pp. 97-112; H. Gharavi et al., "Sub-band Coding of Digital Images Using Two-Dimensional Quadrature Mirror Filter" Proc SPIE, Vol 707, pp 51-61, September 1986; J. W. Woods et al., "Sub-Band Coding of Images" Proc ICASSP, pp 1005-1008, April 1986; H. Gharavi et al., "Application of Quadrature Mirror Filtering to the Coding of Monochrome and Color Images", Proc. ICASSP, Vol. 4, pp. 2384-2387, 1987; P. H. Westerink et al., "Sub-Band Coding of Digital Images Using Predictive Vector Quantization" Proc ICASSP, Vol 3, pp. 1378-1381, 1987). To date, however, substantially exact reconstruction of video signals using the Quadrature Mirror Filter concept has only been achieved through the use of long, multiple stage filter banks which are complex in hardware implementation and are computationally intensive.

A variety of other filter bank designs have been proposed which allow exact, or perfect, reconstruction of various types of sub-band coded signals (see e.g. M. Smith et al., "Exact Reconstruction Techniques for Tree Structured Subband Codes" IEEE Transactions on ASSP, Vol ASSP-34, pp 434-441, June 1986; M. Vetterli, "Filter Bands Allowing Perfect Reconstruction" Signal Processing, Vol. 10, No. 3, pp. 219-244, April 1986). However, these filter bank designs have not proven entirely satisfactory for the perfect reconstruction of sub-band coded video signals because of their high computational complexity. More recently, however, filter banks have been designed which allow for the perfect reconstruction sub-band coded video signals, wherein the individual filters in the analysis and synthesis filter banks are designed to be linear in phase, symmetrical in time, and to have unequal bandwidth frequency responses (see U.S. Pat. No. 4,829,378 by LeGall). Although these non-QMF filter banks are relatively easy to implement in hardware and allow for the perfect reconstruction of sub-band coded video signals with a relatively small amount of computational complexity, the unequal bandwidth frequency responses result in the original signal being disproportionately filtered, decimated, and coded during the decomposition stage, and disproportionately decoded, interpolated, and filtered during the reconstruction stage. As a consequence of the disproportionate filtering, such filter banks exhibit deteriorating frequency responses when used in hierarchical sub-band structures.

Although all of the above-mentioned filter bank designs allow for the sub-band coding of various types of signals, none employ the Quadrature Mirror Filter concept in the design of analysis and synthesis filter banks to the point where hardware implementation is easily obtained and sub-band coding of signals is accomplished with minimal computational complexity so as to result in perfect signal reconstruction. Such analysis and synthesis Quadrature Mirror Filter banks would be desirable since, as previously described, the Quadrature Mirror Filter approach has been shown to be highly effective for signal analysis, synthesis and generation. It would therefore be desirable to provide such analysis and synthesis Quadrature Mirror Filter banks so as to overcome the practical shortcomings of the prior art filter bank designs.

The present invention employs the Multiplierless Quadrature Mirror Filter concept in the design of analysis and synthesis filter banks to be used for the sub-band coding of various types of signals. The individual multiplierless filters in the analysis and synthesis filter banks are designed to be near linear in phase, non-symmetrical in time, and to have equal bandwidth frequency responses. These multiplierless filters are relatively easy to implement in hardware and allow for the sub-band coding of signals with minimal computational complexity so as to result in perfect signal reconstruction. Furthermore, these filters are particularly well suited for configuration in hierarchical sub-band structures. Multiplierless filters have the attribute of minimal computational complexity and relatively easy hardware implementation.

From the above descriptive summary, it is apparent how the Multiplierless Quadrature Mirror Filter concept may be employed in the design of analysis and synthesis filter banks in a manner that allows for relatively easy hardware implementation and that allows for the sub-band coding of various types of signals with minimal computational complexity so as to result in perfect signal reconstruction, thereby overcoming the shortcomings of the prior art filter bank designs.

Accordingly, the primary objective of the present invention is to design analysis and synthesis filter banks by employing the Multiplierless Quadrature Mirror Filter concept in a manner that allows for relatively easy hardware implementation and that allows for the sub-band coding of various types of signals with minimal computational complexity so as to result in perfect signal reconstruction.

Other objectives and advantages of the present invention will become apparent to those skilled in the art upon reading the following detailed description and claims, in conjunction with the accompanying drawings which are appended hereto.

In order to facilitate a fuller understanding of the present invention, reference is now made to the appended drawings. These drawings should not be construed to limit the present invention, but are intended to be exemplary only.

FIG. 1 is a schematic representation of a single-stage signal transmission system incorporating analysis and synthesis Quadrature Mirror Filter banks according to the present invention.

FIG. 2 is a schematic representation of an 8-tap, low pass Perfect Reconstruction Quadrature Mirror Filter according to the present invention.

FIG. 3 shows the phase response of the 8-tap, low pass Perfect Reconstruction Quadrature Mirror Filter shown in FIG. 2.

FIG. 4 shows the magnitude response of the 8-tap, low pass Perfect Reconstruction Quadrature Mirror Filter shown in FIG. 2.

FIG. 5 is a schematic representation of a multiple-stage signal transmission system incorporating analysis and synthesis Quadrature Mirror Filter banks according to the present invention.

Referring to FIG. 1, there is shown a schematic representation of a single-stage signal transmission system 10 for the processing of one-dimensional signals. Included within this one-dimensional signal transmission system 10 are a transmitter section 11 and a receiver section 12 having analysis 13 and synthesis 14 Multiplierless Quadrature Mirror Filter banks respectively, according to the present invention. It should be noted that although only a single-stage signal transmission system 10 is described in detail herein, a multiple-stage signal transmission system for the processing of both one-dimensional and multi-dimensional signals may also be realized by utilizing the present invention Quadrature Mirror Filter banks in a hierarchical sub-band structure. Such a multiple-stage signal transmission system 60 is shown in FIG. 5.

In the single-stage system 10 of FIG. 1, an original discrete time signal, X(z), is input on line 16. This original signal, X(z), is filtered by analysis filters 18a and 18b, which have transfer functions H_{0} (z) and H_{1} (z), respectively. According to the present invention, the analysis filters 18a and 18b are designed to have equal bandwidth frequency responses. Thus, the original signal, X(z), is divided into two equal bandwidth sub-band signals; e.g. a low frequency sub-band signal and a high frequency sub-band signal.

After the original signal, X(z), is filtered, the two resulting signals are decimated by decimation operators 20a and 20b. In the decimation operators 20a and 20b of FIG. 1, the decimation operation is 2:1, meaning that one out of every two sample values in the filtered discrete time signals are removed. This decimation operation allows the transmission rate of the system 10 to remain constant. The resulting filtered and decimated signals are then coded by means of coders 22a and 22b for transmission via lines 24a and 24b, respectively, to the receiver section 12. At this point it should be noted that the filtered and decimated signals may be divided into further sub-bands prior to their being coded. Such further sub-band division is accomplished by further filtering and decimating the signals filtered and decimated. The multiple-stage signal transmission system 60 shown in FIG. 5 would accomplish such further sub-band division thereby allowing multi-resolution. It should be further noted, however, that with every decimation operation a decrease in signal resolution results.

The filtered and decimated signals are individually coded by the coders 22a and 22b. These signals may be coded using any number of conventional coding techniques including, for example, the DCPM technique described in H. Gharavi et al., "Sub-band Coding of Digital Images Using Two Dimensional Quadrature Mirror Filtering" Proc. SPIE Visual Communication and Image Processing, pp. 51-61, September 1986. Since the two signals are equally divided along the frequency spectrum, only one common coding technique need be utilized. Thus, the use of the Multiplierless Quadrature Mirror Filter concept encourages functional duplication within the signal transmission system 10. After the two filtered and decimated signals are coded, they are individually transmitted to the receiver section 12 via lines 24a and 24b.

When the two transmitted signals arrive at the receiver section 12, they are decoded by means of decoders 26a and 26b. The two decoded signals are then interpolated by interpolation operators 28a and 28b. In the interpolation operators 28a and 28b of FIG. 1, the interpolation operation is 1:2, meaning that a sample having a zero value is added between every sample in the decoded discrete time signals. This interpolation operation increases the total number of samples in the decoded discrete time signals by a factor of two, thereby restoring the total number of samples to that of the original signal, X(z).

The two resulting decoded and interpolated signals are filtered by synthesis filters 30a and 30b, which have transfer functions G_{0} (z) and G_{1} (z), respectively. Similar to the analysis filters 18a and 18b, the synthesis filters 30a and 30b are designed to have equal bandwidth frequency responses. Thus, the two resulting filtered signals encompass two equal bandwidth sub-bands; e.g. a low frequency sub-band and a high frequency sub-band, respectively. These two sub-band signals are then summed by an adder circuit 32 so as to produce a discrete time signal, X(z), on line 34 that is a perfect reconstruction of the original signal, X(z), if no quantization or transmission errors occur.

As indicated above, the analysis 13 and synthesis 14 Multiplierless Quadrature Mirror Filter banks are relatively easy to implement in hardware and allow for the sub-band coding of signals with minimal computational complexity so as to result in perfect signal reconstruction. To understand how such multiplierless filter banks 13 and 14 are implemented within the PR-QMF concept, the original signal, X(z), may be traced through the transmitter section 11 and the receiver section 12 of the single-stage system 10 of FIG. 1, so as to arrive at the following expression,

X(a)=T(z)X(z)+S(z)X(-z) (1)

where,

T(z)=[H_{0}(z)G_{0}(z)+H_{1}(z)G_{1}(z)]/2 (2)

S(z)=[H_{0}(-z)G_{0}(z)+H_{1}(-z)G_{1}(z)]/2. (3)

Perfect reconstruction requires that,

i.) S(z)=0; for all z (4)

and,

ii.) T(z)=cz^{-K}; for all z (5)

where c is a constant and K is an integer.

The choice of,

G_{0}(z)=-H_{1}(-z) (6)

and,

G_{1}(z)=H_{0}(-z) (7)

satisfies the first requirement that S(z)=0 and eliminates any aliasing. Next, with N odd, one can choose,

H_{1}(z)=z^{-N}H_{0}(-z^{-1}) (8)

leaving,

T(z)=z^{-N}[H_{0}(z)H_{0}(z^{-1})+H_{0}(-z)H_{0}(-z^{-1})]/2. (9)

With these constraints, the perfect reconstruction requirement reduces to finding an H(z)=H_{0} (z) such that,

H(z)H(z)^{-1})+H(-z)H(z)^{-1})=constant. (10)

This selection implies that all four filters 18a, 18b, 30a, and 30b are causal whenever H_{0} (z) is causal. The above-stated perfect reconstruction requirement can readily be recast in an alternate time domain form as described in A. Akansu et al., "The Binomial QMF-Wavelet Transform for Multiresolution Signal Decomposition", IEEE Transactions on Signal Processing, Vol. 41, No. 1, January 1993, to yield the perfect reconstruction requirement, ##EQU1## where Q is an integer normalization factor and,

δ(k)=1 for k=0 (12)

δ(k)=0 for all other k. (13)

According to the present invention, the individual filters 18a, 18b, 30a, and 30b in the analysis 13 and synthesis 14 filter banks are designed to be near linear in phase, non-symmetrical in time, and to have equal bandwidth frequency responses. In further accord with the present invention, the multiplierless filters are relatively easy to implement in hardware and allow for the sub-band coding of signals with minimal computational complexity. Such filters are obtained by imposing the following binary shift or binary shift and add operational constraints on the prototype low pass analysis filter coefficients given in equation 11, ##EQU2## where,

n=0, 1, . . ., N (15)

where N+1 is the duration of the filter, where,

k_{n}.sup.(i) =integers (16)

and where there is no limit on the value of P in equation 14, although the lower the value of P the higher the efficiency of the filter. Equation 14 defines the multiplierless filter to be embedded in the PR-QMF concept in order to achieve minimal computational complexity and ease of hardware implementation.

Referring to Table 1, the filter coefficients of, for example, 4, 6, 8, and 10-tap, low-pass analysis Multiplierless Perfect Reconstruction Quadrature Mirror Filters (M-PR-QMF's) are listed which were derived in accordance with the above-stated perfect reconstruction requirement and filter coefficient constraints. It should be noted that corresponding filter coefficients for the high-pass analysis filter and the low-pass and high-pass synthesis filters can be derived directly from these low-pass analysis filter coefficients. Note that the filter coefficients in Table 1, and those derived from the filter coefficients in Table 1, are non-symmetrical, thereby effecting a non-linear, although linear-like, phase response, as will be described shortly. Also note that these filter coefficients were derived with P=1, or P=2.

TABLE 1______________________________________h(n)n 10-tap 8-tap 6-tap 4-tap______________________________________0 -1 -8 4 21 -3 8 16 62 9 64 16 33 33 64 0 14 32 8 -45 4 -8 16 -9 17 1 18 39 -1______________________________________ For the 8-tap case, for example, the filter transfer function is expressed as follows,

H_{0}(z)=-8+8z^{-1}+64z^{-2}+64z^{-3}+8z^{-4}-8z^{-5}+z^{-6}+z^{-7}. (17)

Referring to FIG. 2, a schematic representation of the analysis filter 18a having the transfer function expressed in equation 17 above is shown. The filter 18a is comprised of seven stages 40a, 40b, 40c, 40d, 40e, 40f, and 40g, each of which represents a unit time delay, and eight taps 42a, 42b, 42c, 42d, 42e, 42f, 42g, and 42h, each of which maintains a series connected coefficient multiplier 46a, 46b, 46c, 46d, 46e, 46f, 46g, and 46h, and ties into an adder circuit 44. It should be noted that, in accordance with the multiplierless aspect of the present invention, the series connected coefficient multipliers 46a, 46b, 46c, 46d, 46e, 46f, 46g, and 46h do not function as conventional multipliers but as shift operators. An original discrete time signal, X(z), is input to the filter 18a on line 48, where it then propagates through the filter 18a from one stage to the next. This original discrete time signal, X(z), is comprised of a series of digital samples. A filtered discrete time signal, Y(z), is output on line 50. This filtered discrete time signal, Y(z), is formed by adding the present original signal sample, which is multiplied via a shift operation, by its respective coefficient 46a, to the seven previous original signal samples, after each has been multiplied via a shift operation, by their respective coefficients 46b, 46c, 46d, 46e, 46f, 46g, and 46h. Thus, the filtered signal, Y(z), is a linear combination of the present original signal sample and the seven previous original signal samples. Such a filter is classified as a finite impulse response filter.

The filter coefficients 46a, 46b, 46c, 46d, 46e, 46f, 46g, and 46h, are obtained directly from the filter transfer function, H_{0} (z), expressed in equation 17 above. In this transfer function, the z^{-1} term represents a one unit time delay, the z^{-2} term represents a two unit time delay, the z^{-3} term represents a three unit time delay, and so on until the z^{-7} term represents a seven unit time delay. Thus, the filter coefficient 46a of the present original signal sample is -2^{3} or -8, the filter coefficient 46b of the previous original signal sample is 2^{3} or 8, the filter coefficient 46c of the second previous original signal sample is 2^{6} or 64, and so on until the filter coefficient 46h of the seventh previous original signal sample is 2^{0} or 1.

As previously stated, and as can be observed from Table 1, the present invention M-PR-QMF's have filter coefficients that are non-symmetrical in time. Also as previously stated, these filters are easy to implement in hardware and allow for the sub-band coding of signals with minimal computational complexity. Such is the case since all of the filter coefficients are decomposable into power of two integers. This means that filter computations can be carried out using only binary shift or binary shift and add operations, thereby requiring only relatively simple circuitry to carry out these relatively simple filter computations. It should be noted that the 8-tap, low-pass analysis M-PR-QMF 18a having the transfer function expressed in equation 17 above requires only binary shift operations.

Finally, it was also previously stated that the present invention M-PR-QMF's are near linear in phase and have equal bandwidth frequency responses. Referring to FIGS. 3 and 4, there are shown the phase and magnitude responses, respectively, of the 8-tap, low-pass analysis filter 18a having the transfer function expressed in equation 17 above. Although many of the prior art filter designs emphasize the importance of a linear phase response (see U.S. Pat, No. 4,829,378 by LeGall), it has been found that PR-QMF designs favor an equal bandwidth property since it is theoretically impossible to achieve strict phase linearity using the PR-QMF approach. However, as can be seen in FIG. 3, the phase response of filter 18a is only marginally non-linear. Thus, a linear-like phase response can still be achieved using the M-PR-QMF approach.

With the present invention now fully described it can thus be seen that the primary objective set forth above is efficiently attained and, since certain changes may be made in the above described M-PR-QMF design approach without departing from the scope of the invention, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

Patent Citations

Cited Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US4393456 * | Mar 19, 1981 | Jul 12, 1983 | Bell Telephone Laboratories, Incorporated | Digital filter bank |

US4569075 * | Jul 19, 1982 | Feb 4, 1986 | International Business Machines Corporation | Method of coding voice signals and device using said method |

US4652881 * | Jan 10, 1984 | Mar 24, 1987 | Lewis Bernard L | Efficient adaptive filter bank |

US4674125 * | Apr 4, 1984 | Jun 16, 1987 | Rca Corporation | Real-time hierarchal pyramid signal processing apparatus |

US4785348 * | Nov 3, 1987 | Nov 15, 1988 | U.S. Philips Corp. | System for the transmission and reception of high-definition television pictures in narrow-band channels |

US4799179 * | Jan 27, 1986 | Jan 17, 1989 | Telecommunications Radioelectriques Et Telephoniques T.R.T. | Signal analysing and synthesizing filter bank system |

US4815023 * | May 4, 1987 | Mar 21, 1989 | General Electric Company | Quadrature mirror filters with staggered-phase subsampling |

US4829378 * | Jun 9, 1988 | May 9, 1989 | Bell Communications Research, Inc. | Sub-band coding of images with low computational complexity |

US4839889 * | Sep 20, 1988 | Jun 13, 1989 | Ant Nachrichtentechnik Gmbh | Digital filter tree |

US4868868 * | Sep 23, 1987 | Sep 19, 1989 | Oki Electric Industry Co., Ltd. | Sub-band speech analyzing and synthesizing device |

US4918524 * | Mar 14, 1989 | Apr 17, 1990 | Bell Communications Research, Inc. | HDTV Sub-band coding using IIR filter bank |

US5049992 * | Aug 27, 1990 | Sep 17, 1991 | Zenith Electronics Corporation | HDTV system with receivers operable at different levels of resolution |

US5049993 * | Oct 3, 1990 | Sep 17, 1991 | Bell Communications Research, Inc. | Format conversion preprocessing method and circuit |

US5068911 * | Feb 9, 1990 | Nov 26, 1991 | Aware, Inc. | Method and apparatus for representing an image |

US5072308 * | Nov 26, 1990 | Dec 10, 1991 | International Mobile Machines Corporation | Communication signal compression system and method |

US5097331 * | Aug 24, 1990 | Mar 17, 1992 | Bell Communications Research, Inc. | Multiple block-size transform video coding using an asymmetric sub-band structure |

US5101280 * | May 17, 1990 | Mar 31, 1992 | Fuji Photo Film Co., Ltd. | Device for coding a picture signal by compression |

US5128791 * | Aug 13, 1990 | Jul 7, 1992 | Bell Communications Research, Inc. | Multi-channel HDTV system |

US5148498 * | Aug 1, 1990 | Sep 15, 1992 | Aware, Inc. | Image coding apparatus and method utilizing separable transformations |

US5182645 * | Jun 12, 1991 | Jan 26, 1993 | U.S. Philips Corporation | Apparatus for deriving a compatible low-definition interlaced television signal and other components for reconstructing the original signal from an interlaced high-definition television signal |

Non-Patent Citations

Reference | ||
---|---|---|

1 | D. Esteban et al., "Application of Quadrature Mirror Filters, etc." Proceedings of the IEEE International Conference on Acoustics, Speech & Signal Processing (ICASSP), 1977, pp. 191-195. | |

2 | * | D. Esteban et al., Application of Quadrature Mirror Filters, etc. Proceedings of the IEEE International Conference on Acoustics, Speech & Signal Processing (ICASSP), 1977, pp. 191 195. |

3 | H. Gharavi et al., "Application of Quadrature Mirror Filtering to the Coding of Monochrome and Color Images," Proc. ICASSP, vol. 4, 1987, pp. 2384-2387. | |

4 | H. Gharavi et al., "Sub-band Coding of Digital Images Using Two-Dimensional Quadrature Mirror Filter," Proc. SPIE, vol. 707, Sep., 1986, pp. 51-61. | |

5 | * | H. Gharavi et al., Application of Quadrature Mirror Filtering to the Coding of Monochrome and Color Images, Proc. ICASSP, vol. 4, 1987, pp. 2384 2387. |

6 | * | H. Gharavi et al., Sub band Coding of Digital Images Using Two Dimensional Quadrature Mirror Filter, Proc. SPIE, vol. 707, Sep., 1986, pp. 51 61. |

7 | J. W. Woods et al., "Subband Coding of Images," IEEE Transactions on Acoustics, Speech & Signal Processing, vol. ASSP-34, Oct., 1986, pp. 1278-1288. | |

8 | J. W. Woods et al., "Sub-band Coding of Images," Proc. ICASSP, Apr., 1986, 1005-1008. | |

9 | * | J. W. Woods et al., Sub band Coding of Images, Proc. ICASSP, Apr., 1986, 1005 1008. |

10 | * | J. W. Woods et al., Subband Coding of Images, IEEE Transactions on Acoustics, Speech & Signal Processing, vol. ASSP 34, Oct., 1986, pp. 1278 1288. |

11 | M. Smith et al., "Exact Reconstruction Techniques for Tree Structured Subband Codes," IEEE Transactions on ASSP, vol. ASSP-34, Jun., 1986, pp. 434-441. | |

12 | * | M. Smith et al., Exact Reconstruction Techniques for Tree Structured Subband Codes, IEEE Transactions on ASSP, vol. ASSP 34, Jun., 1986, pp. 434 441. |

13 | M. Vetterli, "Filter Bands Allowing Perfect Reconstruction," Signal Processing, vol. 10, No. 3, Apr. 1986, pp. 219-244. | |

14 | M. Vetterli, "Multi-dimensional Sub-band Coding: Some Theory & Algorithms," Signal Processing, 1984, pp. 97-112. | |

15 | * | M. Vetterli, Filter Bands Allowing Perfect Reconstruction, Signal Processing, vol. 10, No. 3, Apr. 1986, pp. 219 244. |

16 | * | M. Vetterli, Multi dimensional Sub band Coding: Some Theory & Algorithms, Signal Processing, 1984, pp. 97 112. |

17 | P. H. Westerlink et al., "Sub-band Coding of Digital Images Using Predictive Vector Quantization," Proc. ICASSP, vol. 3, 1987, pp. 1378-1381. | |

18 | * | P. H. Westerlink et al., Sub band Coding of Digital Images Using Predictive Vector Quantization, Proc. ICASSP, vol. 3, 1987, pp. 1378 1381. |

19 | R. E. Crochiere et al., "Digital Coding of Speech in Sub-bands," BSTJ, vol. 55, pp. 1069-1085. | |

20 | * | R. E. Crochiere et al., Digital Coding of Speech in Sub bands, BSTJ, vol. 55, pp. 1069 1085. |

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Citing Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US5481269 * | May 27, 1994 | Jan 2, 1996 | Westinghouse Electric Corp. | General frame wavelet classifier |

US5497777 * | Sep 23, 1994 | Mar 12, 1996 | General Electric Company | Speckle noise filtering in ultrasound imaging |

US5559834 * | Oct 6, 1992 | Sep 24, 1996 | Edler; Bernd | Method of reducing crosstalk in processing of acoustic or optical signals |

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US5668850 * | May 23, 1996 | Sep 16, 1997 | General Electric Company | Systems and methods of determining x-ray tube life |

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US5748116 * | Nov 27, 1996 | May 5, 1998 | Teralogic, Incorporated | System and method for nested split coding of sparse data sets |

US5832124 * | Mar 28, 1994 | Nov 3, 1998 | Sony Corporation | Picture signal coding method and picture signal coding apparatus, and picture signal decoding method and picture signal decoding apparatus |

US5881176 * | May 3, 1996 | Mar 9, 1999 | Ricoh Corporation | Compression and decompression with wavelet style and binary style including quantization by device-dependent parser |

US5889559 * | Nov 26, 1997 | Mar 30, 1999 | Intel Coproration | Method and apparatus for minimally-shifted wavelet decomposition and recomposition |

US5893100 * | Nov 27, 1996 | Apr 6, 1999 | Teralogic, Incorporated | System and method for tree ordered coding of sparse data sets |

US5907360 * | Mar 4, 1994 | May 25, 1999 | Thomson-Csf | Coder/decoder for television image sub-band compatible coding, and its application to hierarchical motion coding by tree structures |

US5909518 * | Nov 27, 1996 | Jun 1, 1999 | Teralogic, Inc. | System and method for performing wavelet-like and inverse wavelet-like transformations of digital data |

US5966465 * | May 3, 1996 | Oct 12, 1999 | Ricoh Corporation | Compression/decompression using reversible embedded wavelets |

US5999656 * | Jan 17, 1997 | Dec 7, 1999 | Ricoh Co., Ltd. | Overlapped reversible transforms for unified lossless/lossy compression |

US6009434 * | Oct 29, 1998 | Dec 28, 1999 | Teralogic, Inc. | System and method for tree ordered coding of sparse data sets |

US6044172 * | Dec 22, 1997 | Mar 28, 2000 | Ricoh Company Ltd. | Method and apparatus for reversible color conversion |

US6195465 | Jul 3, 1995 | Feb 27, 2001 | Ricoh Company, Ltd. | Method and apparatus for compression using reversible wavelet transforms and an embedded codestream |

US6222941 | Aug 9, 1996 | Apr 24, 2001 | Ricoh Co., Ltd. | Apparatus for compression using reversible embedded wavelets |

US6314452 | Aug 31, 1999 | Nov 6, 2001 | Rtimage, Ltd. | System and method for transmitting a digital image over a communication network |

US6408322 * | Feb 17, 1999 | Jun 18, 2002 | Thomson Licensing S.A. | Apparatus and method for anchoring predetermined points of the impulse frequency response of a physically-realized filter |

US6434192 * | Nov 10, 1998 | Aug 13, 2002 | Matsushita Electric Industrial Co., Ltd. | Adaptive equalizing device |

US6466957 | Sep 2, 1999 | Oct 15, 2002 | 3Com Corporation | Reduced computation system for wavelet transforms |

US6553396 * | Dec 9, 1999 | Apr 22, 2003 | Sony Corporation | Filter bank constituting method and filter bank apparatus |

US6581081 | Jan 24, 2000 | Jun 17, 2003 | 3Com Corporation | Adaptive size filter for efficient computation of wavelet packet trees |

US6668013 | Jul 7, 1999 | Dec 23, 2003 | Sharp Kabushiki Kaisha | Digital filter |

US6826584 * | Dec 22, 2000 | Nov 30, 2004 | Sony Corporation | Refinement of interpolated signals |

US6859563 | Mar 30, 2001 | Feb 22, 2005 | Ricoh Co., Ltd. | Method and apparatus for decoding information using late contexts |

US6873734 | Feb 7, 2000 | Mar 29, 2005 | Ricoh Company Ltd | Method and apparatus for compression using reversible wavelet transforms and an embedded codestream |

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US6925209 | Mar 6, 2001 | Aug 2, 2005 | Ricoh Co., Ltd. | Method and apparatus for outputting a codestream as multiple tile-part outputs with packets from tiles being output in each tile-part |

US6950558 | Mar 30, 2001 | Sep 27, 2005 | Ricoh Co., Ltd. | Method and apparatus for block sequential processing |

US6973217 | Mar 6, 2001 | Dec 6, 2005 | Ricoh Co., Ltd. | Method and apparatus for sending additional sideband information in a codestream |

US6983075 | Mar 6, 2001 | Jan 3, 2006 | Ricoh Co., Ltd | Method and apparatus for performing selective quantization by manipulation of refinement bits |

US6990247 | Jan 8, 2003 | Jan 24, 2006 | Ricoh Co., Ltd. | Multiple coder technique |

US7006697 | Mar 30, 2001 | Feb 28, 2006 | Ricoh Co., Ltd. | Parallel block MQ arithmetic image compression of wavelet transform coefficients |

US7016545 | Nov 1, 2000 | Mar 21, 2006 | Ricoh Co., Ltd. | Reversible embedded wavelet system implementation |

US7024046 | Apr 17, 2001 | Apr 4, 2006 | Real Time Image Ltd. | System and method for the lossless progressive streaming of images over a communication network |

US7054493 | Jan 8, 2003 | May 30, 2006 | Ricoh Co., Ltd. | Context generation |

US7062101 | Mar 30, 2001 | Jun 13, 2006 | Ricoh Co., Ltd. | Method and apparatus for storing bitplanes of coefficients in a reduced size memory |

US7062103 | Mar 6, 2001 | Jun 13, 2006 | Ricoh Co., Ltd. | Method and apparatus for specifying quantization based upon the human visual system |

US7068849 | Aug 22, 2002 | Jun 27, 2006 | Ricoh Co. Ltd. | Method and apparatus for compression using reversible wavelet transforms and an embedded codestream |

US7072520 | Mar 6, 2001 | Jul 4, 2006 | Ricoh Co., Ltd. | Method and apparatus for selecting layers for quantization based on sideband information |

US7076104 | Jan 25, 1999 | Jul 11, 2006 | Ricoh Co., Ltd | Compression and decompression with wavelet style and binary style including quantization by device-dependent parser |

US7079690 | Mar 6, 2001 | Jul 18, 2006 | Ricoh Co., Ltd. | Method and apparatus for editing an image while maintaining codestream size |

US7088869 | Dec 1, 2004 | Aug 8, 2006 | Ricoh Co., Ltd. | 5,3 wavelet filter having three high pair and low pair filter elements with two pairs of cascaded delays |

US7095900 | Mar 6, 2001 | Aug 22, 2006 | Ricoh Co., Ltd. | Method and apparatus for performing scalar quantization with a power of two step size |

US7095907 | Jan 10, 2002 | Aug 22, 2006 | Ricoh Co., Ltd. | Content and display device dependent creation of smaller representation of images |

US7120305 | Apr 16, 2002 | Oct 10, 2006 | Ricoh, Co., Ltd. | Adaptive nonlinear image enlargement using wavelet transform coefficients |

US7139434 | Jan 8, 2003 | Nov 21, 2006 | Ricoh Co., Ltd. | Decoding with storage of less bits for less important data |

US7164804 | Mar 15, 2005 | Jan 16, 2007 | Ricoh Co., Ltd. | Method and apparatus for eliminating flicker by quantizing values based on previous quantization |

US7167589 | Jan 8, 2003 | Jan 23, 2007 | Ricoh Co., Ltd. | Disk read technique |

US7167592 | Aug 22, 2002 | Jan 23, 2007 | Ricoh Co., Ltd. | Method and apparatus for compression using reversible wavelet transforms and an embedded codestream |

US7215820 | Jan 10, 2003 | May 8, 2007 | Ricoh Co., Ltd. | Method and apparatus for compression using reversible wavelet transforms and an embedded codestream |

US7227999 | Dec 12, 2002 | Jun 5, 2007 | Ricoh Co., Ltd. | Printing system application using J2K |

US7280252 | Dec 19, 2001 | Oct 9, 2007 | Ricoh Co., Ltd. | Error diffusion of multiresolutional representations |

US7289677 | Jan 8, 2003 | Oct 30, 2007 | Ricoh Co., Ltd. | Reversible embedded wavelet system implementation |

US7298912 | Dec 13, 2005 | Nov 20, 2007 | Ricoh Co., Ltd. | Method and apparatus for assigning codeblocks to coders operating in parallel |

US7321695 | Dec 12, 2002 | Jan 22, 2008 | Ricoh Co., Ltd. | Encoder rate control |

US7362816 * | Apr 28, 2003 | Apr 22, 2008 | Xtendwave, Inc. | Inversion of channel distortion by adaptive wavelet lifting |

US7376279 | Dec 14, 2001 | May 20, 2008 | Idx Investment Corporation | Three-dimensional image streaming system and method for medical images |

US7397963 | Feb 27, 2006 | Jul 8, 2008 | Ricoh Co., Ltd. | Method and apparatus for storing bitplanes of coefficients in a reduced size memory |

US7418142 | Sep 30, 1997 | Aug 26, 2008 | Ricoh Company, Ltd. | Method for compression using reversible embedded wavelets |

US7454074 | Jul 18, 2005 | Nov 18, 2008 | General Electric Company | System and method for the lossless progressive streaming of images over a communication network |

US7457473 | Jun 15, 2005 | Nov 25, 2008 | Ricoh Co., Ltd. | Method for block sequential processing |

US7474791 | Jan 17, 2006 | Jan 6, 2009 | Ricoh Co., Ltd. | Content and display device dependent creation of smaller representations of images |

US7477792 | Mar 6, 2001 | Jan 13, 2009 | Ricoh Co., Ltd. | Method and apparatus for performing progressive order conversion |

US7581027 | Jun 27, 2001 | Aug 25, 2009 | Ricoh Co., Ltd. | JPEG 2000 for efficent imaging in a client/server environment |

US7634145 | May 30, 2006 | Dec 15, 2009 | Ricoh Co., Ltd. | Compression and decompression with wavelet style and binary style including quantization by device-dependent parser |

US8144803 | Apr 18, 2008 | Mar 27, 2012 | Xw, Llc | Inversion of channel distortion by adaptive wavelet lifting |

US8565298 | Oct 30, 2007 | Oct 22, 2013 | Ricoh Co., Ltd. | Encoder rate control |

US8588305 * | Jun 20, 2008 | Nov 19, 2013 | Nvidia Corporation | Two-dimensional interpolation architecture for motion compensation in multiple video standards |

US8924900 * | Apr 11, 2013 | Dec 30, 2014 | Chung Yuan Christian University | Analytical synthesis method and otra-based circuit structure |

US20010047516 * | Jan 31, 2001 | Nov 29, 2001 | Compaq Computer Corporation | System for time shifting live streamed video-audio distributed via the internet |

US20040103133 * | Nov 27, 2002 | May 27, 2004 | Spectrum Signal Processing Inc. | Decimating filter |

US20040120585 * | Mar 6, 2001 | Jun 24, 2004 | Schwartz Edward L. | Method and apparatus for sending additional sideband information in a codestream |

US20050143973 * | Jan 25, 2005 | Jun 30, 2005 | Matsushita Electric Industrial Co., Ltd. | Digital signal sub-band separating/combining apparatus achieving band-separation and band-combining filtering processing with reduced amount of group delay |

US20050185851 * | Dec 1, 2004 | Aug 25, 2005 | Yutaka Satoh | 5,3 wavelet filter |

US20050271283 * | Jul 18, 2005 | Dec 8, 2005 | Shai Dekel | System and method for the lossless progressive streaming of images over a communication network |

US20090168885 * | Jun 20, 2008 | Jul 2, 2009 | Yong Peng | Two-dimensional interpolation architecture for motion compensation in multiple video standards |

EP0975091A2 * | Jul 2, 1999 | Jan 26, 2000 | Sharp Corporation | Digital filter |

WO1998024012A1 * | Nov 10, 1997 | Jun 4, 1998 | Teralogic Inc | System and method for tree ordered coding of sparse data sets |

Classifications

U.S. Classification | 375/350, 708/313, 375/229, 375/240.11, 375/240, 708/319 |

International Classification | H03H17/02, H04B1/66 |

Cooperative Classification | H04B1/667, H03H17/0266 |

European Classification | H04B1/66S, H03H17/02F8A |

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Dec 22, 1998 | REMI | Maintenance fee reminder mailed | |

May 30, 1999 | LAPS | Lapse for failure to pay maintenance fees | |

Jul 27, 1999 | FP | Expired due to failure to pay maintenance fee | Effective date: 19990530 |

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